Analytical solution for the modified nonlinear Schrödinger equation describing optical shock formation

Abstract

We present an exact analytical solution by the use of an ansatz method for the modified nonlinear Schrödinger equation iU ϩ 1 2 U ϩN 2 ͉U͉ 2 UϩisN 2 (͉U͉ 2 U) ϭ0, describing the propagation of light pulses in optical fibers. The inclusion of the term isN 2 (͉U͉ 2 U) in the usual nonlinear Schrödinger equation arises from an intensity-dependent group velocity and produces a temporal pulse distortion leading to the development of an optical shock. Previous work ͓Xu Bingzhen and Wang Wenzheng, Phys. Rev. E 51, 1493 ͑1995͔͒ using the traveling-wave method does not exhibit this important physical picture. ͓S1063-651X͑98͒05004-1͔

Kink Waves in an Extended Nonlinear Schrödinger Equation with Allowance for Stimulated Scattering and Nonlinear Dispersion

“…These terms correspond to the nonlinear effects of steepening [11] and stimulated scattering [12], and to the linear effect of an aberrational distortion corresponding to the third-order linear dispersion. The equation resulting from this allowance is conventionally called the extended nonlinear Schrödinger equation earlier, the stationary waves were studied in [13,14] within the framework of this equation with allowance only for stimulated scattering, disregarding nonlinear dispersion and the third-order linear dispersion.…”

Breather and double-pole solutions of the derivative nonlinear Schrödinger equation from optical fibers

“…Knowing that the formation mechanism and interaction dynamics of the dark and anti-dark solitons in the normal dispersion regime have been obtained in Ref. [18], in this Letter, we will investigate the breather and double-pole solutions of the following derivative nonlinear Schrödinger (DNLS) equation [19][20][21]:…”

A Coupled Higher-Order Nonlinear Schrodinger Equation Including Higher-Order Bright and Dark Solitons

“…After a huge amount of study for the practical applications as well as for the academic interest, several soliton field experiments of 10 Gbps ∼ 40 Gbps communications have been carried out recently in Japan, USA, and Europe [3], respectively. For a higher rate transmission of pulses, the wavelength division multiplexing [4] could be also taken into account to conduct the soliton transmission experiment of 1 Tbps level in a laboratory [5].In the ultrafast optical soliton system where a pulse is in general shorter than T 0 ≤ 100 fs [4], higher-order effects such as the third-order dispersion [6], the selfsteepening [7], and the self-frequency shift [8] need to be considered for the propagation of femtosecond pulses in a monomode optical fiber. Regarding the Hirota [9] and the Sasa-Satsuma [10] equations which are known to be the only two integrable types of the higher-order NSEs, the Painlevé integrability property [11], [12], an exact N -soliton solution [13], and solitary wave and shock solutions in the generalized phase function have been found [14].…”

“…In the ultrafast optical soliton system where a pulse is in general shorter than T 0 ≤ 100 fs [4], higher-order effects such as the third-order dispersion [6], the selfsteepening [7], and the self-frequency shift [8] need to be considered for the propagation of femtosecond pulses in a monomode optical fiber. Regarding the Hirota [9] and the Sasa-Satsuma [10] equations which are known to be the only two integrable types of the higher-order NSEs, the Painlevé integrability property [11], [12], an exact N -soliton solution [13], and solitary wave and shock solutions in the generalized phase function have been found [14].…”